CHAPTER 11 • Pricing with Market Power 445 conditions of marginal analysis: The output of each upstream division should be such that its marginal cost is equal to its marginal contribution to the profit of the overall firm Now, what transfer prices P1 and P2 should be “charged” to the downstream division for its use of the intermediate inputs? Remember that if each of the three divisions uses these transfer prices to maximize its own divisional profit, the profit of the overall firm should be maximized The two upstream divisions will maximize their divisional profits, p1 and p2, which are given by p1 = P1Q1 - C1(Q1) and p2 = P2Q2 - C2(Q2) Because the upstream divisions take P1 and P2 as given, they will choose Q1 and Q2 so that P1 ϭ MC1 and P2 ϭ MC2 Similarly, the downstream division will maximize p(Q) = R(Q) - Cd(Q) - P1Q1 - P2Q2 Because the downstream division also takes P1 and P2 as given, it will choose Q1 and Q2 so that (MR - MCd)MP1 = NMR1 = P1 (A11.18) (MR - MCd)MP2 = NMR2 = P2 (A11.19) and Note that by setting the transfer prices equal to the respective marginal costs (P1 ϭ MC1 and P2 ϭ MC2), the profit-maximizing conditions given by equations (A11.16) and (A11.17) will be satisfied We therefore have a simple solution to the transfer pricing problem: Set each transfer price equal to the marginal cost of the respective upstream division Then when each division is required to maximize its own profit, the quantities Q1 and Q2 that the upstream divisions will want to produce will be the same quantities that the downstream division will want to “buy,” and they will maximize the firm’s total profit To illustrate this graphically, suppose Race Car Motors, Inc., has two divisions The upstream Engine Division produces engines, and the downstream Assembly Division puts together automobiles, using one engine (and a few other parts) in each car In Figure A11.2, the average revenue curve AR is Race Car Motors’ demand curve for cars (Note that the firm has monopoly power in the automobile market.) MCA is the marginal cost of assembling automobiles, given the engines (i.e., it does not include the cost of the engines) Because the car requires one engine, the marginal product of the engines is one Thus the curve labeled MR − MCA is also the net marginal revenue curve for engines: NMRE = (MR - MCA)MPE = MR - MCA The profit-maximizing number of engines (and number of cars) is given by the intersection of the net marginal revenue curve NMRE with the marginal cost curve for engines MCE Having determined the number of cars that it will produce, and knowing its divisional cost functions, the management of Race Car